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A difference equation is an equation where the unknown is a function f that occurs in the equation through f(x), f(x−1), ..., f(x−k), for some whole integer k called the order of the equation. If x is restricted to be an integer, a difference equation is the same as a recurrence relation
This is a list of equations, by Wikipedia page under appropriate bands of their field. Eponymous equations The following equations are named after researchers who ...
The phrase "linear equation" takes its origin in this correspondence between lines and equations: a linear equation in two variables is an equation whose solutions form a line. If b ≠ 0 , the line is the graph of the function of x that has been defined in the preceding section.
A typical such equation is the equation of Fermat's Last Theorem x d + y d − z d = 0. {\displaystyle x^{d}+y^{d}-z^{d}=0.} As a homogeneous polynomial in n indeterminates defines a hypersurface in the projective space of dimension n − 1 , solving a homogeneous Diophantine equation is the same as finding the rational points of a projective ...
Schrödinger–Newton equation; Segregated Runge–Kutta methods; Seneca effect; Septic equation; Sextic equation; Simon–Glatzel equation; Slutsky equation; Solution in radicals; Solution set; Solving quadratic equations with continued fractions; Souders–Brown equation; Spherical wave transformation; Stokesian dynamics; Sunrise equation ...
This equation states that , representing the square of the length of the side that is the hypotenuse, the side opposite the right angle, is equal to the sum (addition) of the squares of the other two sides whose lengths are represented by a and b. An equation is the claim that two expressions have the same value and are equal.
Note that even simple equations like = are solved using cross-multiplication, since the missing b term is implicitly equal to 1: =. Any equation containing fractions or rational expressions can be simplified by multiplying both sides by the least common denominator.
A differential equation is a mathematical equation for an unknown function of one or several variables that relates the values of the function itself and its derivatives of various orders. [21] [22] [23] Differential equations play a prominent role in engineering, physics, economics, biology, and other disciplines.